Prediction of spinel structure and properties of single and double nitrides

Abstract

Lattice constants, bulk moduli, band gaps, electronic bonding, and the stability of 20 new nitrides with spinel structure are studied by first-principles calculations. Double nitrides AB 2 N 4 are found to be stable when the counterparts BA 2 N 4 are metastable except for TiZr 2 N 4 . The four single nitrides C 3 N 4 , Si 3 N 4 , Ge 3 N 4 , and Sn 3 N 4 have direct band gaps at the ⌫ point ranging from 1.14 to 3.45 eV while Zr 3 N 4 and Ti 3 N 4 have small indirect gaps. For double nitrides, both metallic and insulating band structures are possible. The total bond orders of the stable double nitrides are larger than those of constituent single nitrides. Among them, CSi 2 N 4 shows exceptionally strong covalent bonding and a large bulk modulus. A simple scaling law based on bond lengths can describe the bulk moduli of these spinel nitrides quite well.

Origin of the low compressibility in hard nitride spinels

“…This is a critical requirement from an energetic perspective for the synthesis of ␥-C 3 N 4 . The C t -N bond is stronger than the C o -N one, in agreement with the bond orders calculated by Ching et al, 4 and can be seen as a consequence of the shorter C-N distance at the tetrahedral sites. There is no contradiction between the C-N bond strengths and the values of the bulk moduli of CN 4 and CN 6 since the number of C-N bonds involved in the polyhedra have also to be considered.…”

“…Numerical and Vinet analytical 22 fittings to the resulting E crys versus V curve were performed to obtain the EOS and the u( p) relationship. Atomiclike EOS and AN 4 and AN 6 polyhedral EOS were then evaluated using V( P) and u( p) values, and the equations V t ϭ8V(uϪ1/8) 3 /3 and V o ϭ16V(uϪ3/8) 2 u/3 ͑see Refs. 18 and 23 for more details͒.…”

“…The atomic volumes and compressibilities are additive and recover the corresponding bulk values. 17 This simple partition is also related here to the more usual decomposition in terms of the elementary AN 4 and AN 6 polyhedra of the cubic spinel structures. 18 As a result, the linking between compressibility and chemical bonding is clearly established, and factors determining the difficulty in the synthesis of ␥-A 3 N 4 polymorphs are also derived.…”

“…1 The search for these compounds is mainly guided by the empirical trends found in the pressure ͑p͒ response of a variety of binary and ternary crystals. This systematic behavior has prompted the proposal of simple correlations involving coordination polyhedral volumes 2 or nearest-neighbor distances 3,4 along with some bonding index as the key parameters to estimate bulk moduli ͑B͒ of solids. In tetrahedrally bonded compounds, the success of Cohen's equation 3 has fueled the investigation of carbon nitride polymorphs [5][6][7][8] since it predicts B values significantly larger than diamond.…”

“…For example, contrarily to the uniform behavior of general AB 2 O 4 spinels with zero pressure bulk moduli (B 0 ) clustering around 200 GPa, nitride spinels are predicted to have B 0 values ranging from 200 to 400 GPa. 4 Experimental and theoretical works have identified these cubic high-pressure polymorphs as a new class of potential superhard materials ͑see, for example, Refs. 4, 9-14, and references therein͒.…”